I play the game on a PC. I can't use my mouse to drive.

I am right handed and I have tried that hand, my left hand and a combination of both. I come in last in races and It takes me more time to do one lap than the time you have to do three.

I have killed some cars in the wasteland but got no credit for that.

No amount practice will help me.

Is there a work around or cheat to get race certificates to upgrade the car so I can continue on missions.

I did it using my face

http://www.youtube.com/watch?v=5qysiBWtV-Q

If you're using the default WASD setup, you can try remapping the keys to the arrow keys - I found that much easier to use with my right hand. Shift was a good choice for Boost, and I didn't even bother with braking.

Racing does take a bit of practice, but you will be able to get there (and believe me, I svcked just as badly at it too). It's unfortunate that the first main race you can enter is the Dusty 8 time trial, as that course can be quite a bit winding and tortuous. The trick is to keep on the track and Boost at the start of each straight stretch; you should easily come under the time after a few attempts. Once you beat it, you can go to Sally in the bar and you'll be able to pick up certs from her for killing bandits; that should get you good enough to get rockets too, and from there you can do the Southern Highway race, which is just a matter of Boosting to keep ahead of everyone else and letting the competition destroy each other. Easy win, and a very straight track most of the way.